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A189639 Numbers n such that n'' = n'+1 where n' and n'' are respectively the first and the second arithmetic derivative of n (A003415).

%I A189639 #27 Mar 07 2018 13:24:38
%S A189639 161,209,221,1935,4265,15941,22217,24041,25637,30377,38117,39077,
%T A189639 48617,49097,55877,68441,73817,76457,80357,88457,95237,98117,99941,
%U A189639 105641,110057,115397,122537,130217,131141,136517,143237,147941,148697,152357,154457,159077
%N A189639 Numbers n such that n'' = n'+1 where n' and n'' are respectively the first and the second arithmetic derivative of n (A003415).
%C A189639 The arithmetic derivative of a(n) is a Giuga's number A007850 (solution of n' = n+1).
%H A189639 Reinhard Zumkeller and Donovan Johnson, <a href="/A189639/b189639.txt">Table of n, a(n) for n = 1..1000</a> (first 100 terms from Reinhard Zumkeller)
%e A189639 161' = 30, 161'' = 30' = 31 ==> 161'' = 161'+1 so 161 is a term.
%o A189639 (PARI) /* using _Michael B. Porter_'s code from A003415: */
%o A189639 A003415(n) = {local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))} /* arithmetic derivative */
%o A189639 for(n=1,10^6,d1=A003415(n);d2=A003415(d1);if(d2==d1+1,print1(n,", "))); /* show terms */
%o A189639 /* _Joerg Arndt_, Apr 25 2011 */
%o A189639 (Haskell)
%o A189639 import Data.List (elemIndices)
%o A189639 a189710 n = a189710_list !! (n-1)
%o A189639 a189710_list = elemIndices 0 $
%o A189639    zipWith (-) (map a003415 a003415_list) (map pred a003415_list)
%o A189639 -- _Reinhard Zumkeller_, May 09 2011
%Y A189639 Cf. A003415, A007850, A054377, A132632, A189639.
%K A189639 nonn,look
%O A189639 1,1
%A A189639 _Giorgio Balzarotti_, Apr 24 2011